The value function of singularly perturbed control systems

Z. Artstein*, V. Gaitsgory

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

56 Citations (Scopus)


The limit as ε → 0 of the value function of a singularly perturbed optimal control problem is characterized. Under general conditions it is shown that limit value functions exist and solve in a viscosity sense a Hamilton-Jacobi equation. The Hamiltonian of this equation is generated by an infinite horizon optimization on the fast time scale. In particular, the limit Hamiltonian and the limit Hamilton-Jacobi equation are applicable in cases where the reduction of order, namely setting ε = 0, does not yield an optimal behavior.

Original languageEnglish
Pages (from-to)425-445
Number of pages21
JournalApplied Mathematics and Optimization
Issue number3
Publication statusPublished - May 2000
Externally publishedYes


  • Hamilton-jacobi equation
  • Limit hamiltonian
  • Optimal control
  • Singular perturbation


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